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Determine the equation for the tangent to the curve f(x)=In(1+e') when the tangent is parallel to the line x-2y = 0.

Determine the equation for the tangent to the curve f(x)=In(1+e') when the tangent is parallel to the line x-2y = 0.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 33CT
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F1 2 3. For the function y=x² In x, determine the critical values if x > 0. APPLICATION 4. The amount of radioactive carbon-14 left in a sample of biological material over time is given by the in 2 equation A=10e 5700 where A is the amount of carbon-14 in grams, and t is the time in years. Determine the rate that the carbon-14 is decomposing when there are 4 grams remaining. Decimals allowed. 5. Determine the equation for the tangent to the curve f(x)=In(1+e') when the tangent is parallel to the line x-2y = 0. 6. The tension in a rope that is being used to drag an object with a mass 100 kg across the floor is given by the equation below where T is tension in Newtons and is the angle between the rope and the surface. (Friction has already been factored into the equation.) Determine the angle that minimizes the tension in the rope (to the nearest hundredth of a radian). Remember to check. T 3000 3sin0+4cos THINKING F2 7. The concentration, C in milligrams per litre, of a tracer chemical in the bloodstream t hours after its injection is given by the formula C (t) = e-t-e-³t. Determine the maximum concentration of the chemical and when this occurs. Decimals permitted. #3 80 0≤0</ F3 000 000 $ 4 F4 % 5 SAA F5 MacBook Air > 6 F6 ◄◄ & 7 F7 ► 11 * 8 F8
Transcribed Image Text:F1 2 3. For the function y=x² In x, determine the critical values if x > 0. APPLICATION 4. The amount of radioactive carbon-14 left in a sample of biological material over time is given by the in 2 equation A=10e 5700 where A is the amount of carbon-14 in grams, and t is the time in years. Determine the rate that the carbon-14 is decomposing when there are 4 grams remaining. Decimals allowed. 5. Determine the equation for the tangent to the curve f(x)=In(1+e') when the tangent is parallel to the line x-2y = 0. 6. The tension in a rope that is being used to drag an object with a mass 100 kg across the floor is given by the equation below where T is tension in Newtons and is the angle between the rope and the surface. (Friction has already been factored into the equation.) Determine the angle that minimizes the tension in the rope (to the nearest hundredth of a radian). Remember to check. T 3000 3sin0+4cos THINKING F2 7. The concentration, C in milligrams per litre, of a tracer chemical in the bloodstream t hours after its injection is given by the formula C (t) = e-t-e-³t. Determine the maximum concentration of the chemical and when this occurs. Decimals permitted. #3 80 0≤0</ F3 000 000 $ 4 F4 % 5 SAA F5 MacBook Air > 6 F6 ◄◄ & 7 F7 ► 11 * 8 F8
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